Reference : Diffusion semigroup on manifolds with time-dependent metrics
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/22994
Diffusion semigroup on manifolds with time-dependent metrics
English
Cheng, Li Juan mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Jul-2017
Forum Mathematicum
Walter de Gruyter GmbH & Co. KG.
29
4
751-1002
Yes (verified by ORBilu)
0933-7741
1435-5337
[en] Functional inequalities ; Curvature ; Evolving metric
[en] Let $L_t:=\Delta_t +Z_t $, $t\in [0,T_c)$ on a differential manifold equipped with a complete geometric flow $(g_t)_{t\in [0,T_c)}$, where $\Delta_t$ is the Laplacian operator induced by the metric $g_t$ and $(Z_t)_{t\in [0,T_c)}$ is a family of $C^{1,\infty}$-vector fields. In this article, we present a number of equivalent inequalities for the lower bound curvature condition, which include gradient inequalities, transportation-cost inequalities, Harnack inequalities and other functional inequalities for the semigroup associated with diffusion processes generated by $L_t$. To this end, we establish the derivative formula for the associated semigroup and construct couplings for these diffusion processes by parallel displacement and reflection.
Fonds National de la Recherche Luxembourg
Researchers ; Professionals
http://hdl.handle.net/10993/22994
10.1515/forum-2015-0049
FnR ; FNR7628746 > Anton Thalmaier > GEOMREV > Geometry Of Random Evolutions > 01/03/2015 > 28/02/2018 > 2014

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